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Vali

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View attachment 8746

I tried to use integration by parts.

I took f(x)=arctan(x) => f'(x)= 1/x^2+1

g'(x)=cos(nx) => g(x)= sin(nx)/n

So I get sin(nx)/n * arctan(x) - integral from 0 to 1 from sin(nx)/n(x^2+1)

How to continue ?

I'm always getting stuck with this kind of exercises ( limits of integrals ) because I don't know how to replace n (infinity) in functions and I noticed that I have to use intervals and inequalities to resolve this kind of limits.

Some ideas?

I tried to use integration by parts.

I took f(x)=arctan(x) => f'(x)= 1/x^2+1

g'(x)=cos(nx) => g(x)= sin(nx)/n

So I get sin(nx)/n * arctan(x) - integral from 0 to 1 from sin(nx)/n(x^2+1)

How to continue ?

I'm always getting stuck with this kind of exercises ( limits of integrals ) because I don't know how to replace n (infinity) in functions and I noticed that I have to use intervals and inequalities to resolve this kind of limits.

Some ideas?

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